The invention is based on a fuel injection pump of the type revealed hereinafter. A fuel injection pump is already known wherein the normally rpm-dependent fuel pressure, which changes the onset of the injection, can be changed by a valve operating in accordance with temperature. By this change the onset of the injection is displaced towards "early" during cold starting to such a degree that sufficient time remains for the preparation of the fuel and a correspondingly better ignition or combustion can take place. Here the ambient temperature or the coolant temperature is taken into consideration. It is furthermore known to dispose an adaptation device on fuel injection pumps determining the position of the full-load stop, which acts on a control arm connected with the supply volume adjustment element of the fuel injection pump, and limits its adjusting path for the setting of the maximally permissible full-load supply volume. The simultaneous action of these two devices, the so-called cold start acceleration device and the hydraulic adaptation device for the compensation of the maximally permissible full load supply volume, is not possible since the cold start acceleration device causes pressure changes in the suction chamber of the fuel injection pump which result in unwanted volume changes by the hydraulic adaptation device in a cold internal combustion engine.